I am self-studying topology.I encountered the definition of a paracompact space.A collection $\mathcal A$ of subsets of $X$ is said to be locally finite if each point in $X$ has an open neighborhood that intersects only finitely many members of the collection.Then comes the definition of paracompact space.A space $X$ is said to be paracompact if every open cover has a locally finite open refinement.I want to know what is the motivation behind such a weird definition.I want to know what gave rise to the study of paracompactness,not historically but rather I want to get an intuition behind these things.Can someone help me?
2026-02-23 10:04:42.1771841082
Motivation behind the definition of paracompact.
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